Auxiliary Circle
Category : JEE Main & Advanced
The circle described on the major axis of an ellipse as diameter is called an auxiliary circle of the ellipse.
If \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] is an ellipse, then its auxiliary circle is \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\].
Eccentric angle of a point: Let P be any point on the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]. Draw PM perpendicular from P on the major axis of the ellipse and produce MP to meet the auxiliary circle in Q. Join CQ. The angle \[\angle XCQ=\varphi \] is called the eccentric angle of the point P on the ellipse.
Note that the angle \[\angle XCP\] is not the eccentric angle of point P.
You need to login to perform this action.
You will be redirected in
3 sec
